A Pack of 52 cards is given
By using the formula of probability, we get,
P (E) = favourable outcomes / total possible outcomes
We know, a card is drawn from a pack of 52 cards, so number of elementary events in the sample space will be,
$n(S)={}^{52}C_1=52$
(i) Let E be the event of drawing not a diamond card
Let E′ as the event that diamond card appears
$n (E^{′}) ={}^{13}C_1=13$
P (E′) = n (E′) / n (S)
= 13 / 52
= 1/4
So, P (E) = 1 – P (E′)
= 1 – 1/4
= 3/4
(ii) Let E be the event of drawing a black card
$n (E) ={}^{26}C_1 = 26$ (spades and clubs)
P (E) = n (E) / n (S)
= 26 / 52
= 1/2